Model-independent superhedging under portfolio constraints

Fahim, Arash; Huang, Yu‐Jui

doi:10.1007/s00780-015-0284-9

Cited by 17 publications

(4 citation statements)

References 30 publications

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“…Several authors considered setups with frictions, e.g. transactions costs in Dolinsky and Soner [24] or trading constraints in Cox et al [16] and Fahim and Huang [28].…”

Section: Short Literature Reviewmentioning

confidence: 99%

Robust pricing–hedging dualities in continuous time

Hou

Obłój

2018

Finance Stoch

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We pursue a robust approach to pricing and hedging in mathematical finance. We consider a continuous-time setting in which some underlying assets and options, with continuous price paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland (Ann. Stat. 31:1413Stat. 31: -1438Stat. 31: , 2003, we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. superreplication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows us to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices of an exotic option with payoff G is equal to the supremum of expectations of G under calibrated martingale measures. Our results include in particular the martingale optimal transport duality of Dolinsky and Soner (Probab. Theory Relat. Fields 160:391-427, 2014) and extend it to multiple dimensions, multiple maturities and beliefs which are invariant under time-changes. In a general setting with arbitrary beliefs and for a uniformly continuous G, the asserted duality holds between limiting values of perturbed problems.

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“…Several authors considered setups with frictions, e.g. transactions costs in Dolinsky and Soner [24] or trading constraints in Cox et al [16] and Fahim and Huang [28].…”

Section: Short Literature Reviewmentioning

confidence: 99%

Robust pricing–hedging dualities in continuous time

Hou

Obłój

2018

Finance Stoch

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“…For examples of markets with various kinds of portfolio constraints, we refer to Carassus et al (2001), Fahim and Huang (2016), Karatzas and Kou (1996,1998), and Pulido (2014 and the references therein. The concept of a constrained portfolio should be contrasted with the notion of admissibility of a trading strategy that may involve some additional conditions imposed on the wealth process and thus indirectly also on the class of admissible processes φ (see Definition 8).…”

Section: Self-financing Trading Strategiesmentioning

confidence: 99%

Arbitrage-free pricing of derivatives in nonlinear market models

Bielecki

Cialenco

Rutkowski

2018

Probab Uncertain Quant Risk

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which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Abstract The objective of this paper is to provide a comprehensive study of the no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as collateralization and capital requirements. To achieve our goals, we extend in several respects the nonlinear pricing approach developed in (El Karoui and Quenez 1997) and , which was subsequently continued in (Bielecki and Rutkowski 2015).

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“…The "usual" setting of semi-static hedging (see for instance, [14,8,4,1,5,11,12,2] and the references there in) assumes that the investor makes her decision with full access to the prices of the assets. In this work we consider the case where the investment decisions are based only on delayed information, and the actual present asset price is unknown at the time of decision making.…”

Section: Introductionmentioning

confidence: 99%

Martingale Optimal Transport and Robust Hedging in Continuous Time

Dolinsky

Soner

2013

SSRN Journal

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Abstract. The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

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Model-independent superhedging under portfolio constraints

Cited by 17 publications

References 30 publications

Robust pricing–hedging dualities in continuous time

Robust pricing–hedging dualities in continuous time

Arbitrage-free pricing of derivatives in nonlinear market models

Martingale Optimal Transport and Robust Hedging in Continuous Time

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